file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Data/Multiset/Dedup.lean | Multiset.dedup_le | [] | [
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57
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Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.exists_zigzag' | [] | [
333,
69
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_prod_Icc | [
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Mathlib/Topology/PartitionOfUnity.lean | PartitionOfUnity.continuous_smul | [] | [
186,
76
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.ofRat_inv | [
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269,
74
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.LHom.setOf_realize_onFormula | [
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Mathlib/CategoryTheory/Preadditive/OfBiproducts.lean | CategoryTheory.SemiadditiveOfBinaryBiproducts.add_eq_right_addition | [] | [
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6
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Mathlib/Data/Real/EReal.lean | EReal.coe_pow | [] | [
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1198,
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.degree_map_eq_of_injective | [
{
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334,
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Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | DifferentiableWithinAt.exp | [] | [
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50
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292,
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.coe_injective | [
{
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1431,
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Mathlib/Logic/Equiv/Defs.lean | Equiv.Perm.sigmaCongrRight_symm | [] | [
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.le_of_add_le_add_right | [
{
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.one_compContinuous | [] | [
647,
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646,
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Mathlib/Analysis/Convex/Extrema.lean | IsMinOn.of_isLocalMin_of_convex_univ | [] | [
83,
95
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Mathlib/Order/Filter/Basic.lean | Filter.filter_eq | [] | [
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43
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Mathlib/Topology/DenseEmbedding.lean | DenseInducing.continuousAt_extend | [
{
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216,
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Mathlib/RingTheory/SimpleModule.lean | covby_iff_quot_is_simple | [
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88,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean | EulerSine.sin_pi_mul_eq | [
{
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271,
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.prod_top | [
{
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1070,
53
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.Minpoly.toAdjoin.surjective | [
{
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Mathlib/Data/Int/Dvd/Pow.lean | Int.sign_pow_bit1 | [] | [
28,
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Mathlib/Algebra/Order/Floor.lean | Int.preimage_Iic | [
{
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isInt_eq_false | [
{
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{
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702,
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderBaseChange.baseChange_map | [
{
"state_after": "C : Type u\ninst✝² : Category C\nD : Type ?u.24086\ninst✝¹ : Category D\ninst✝ : HasPullbacks C\nP : MorphismProperty C\nhP : StableUnderBaseChange P\nS S' : C\nf : S' ⟶ S\nX Y : Over S\ng : X ⟶ Y\nH : P g.left\ne : pullback g.left pullback.fst ≅ pullback X.hom f :=\n pullbackRightPullbackFst... | [
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Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.subset_closure | [] | [
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86
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Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_pow | [
{
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{
... | [
256,
85
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Mathlib/Topology/Basic.lean | continuousAt_id | [] | [
1701,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1700,
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Mathlib/LinearAlgebra/InvariantBasisNumber.lean | card_le_of_injective' | [
{
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124,
46
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_algebraMap | [] | [
415,
63
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414,
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Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.map_sup | [
{
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}
] | [
98,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
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Mathlib/SetTheory/Game/PGame.lean | PGame.sub_zero | [
{
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}
] | [
1605,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1604,
1
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Mathlib/Data/Num/Lemmas.lean | PosNum.to_int_eq_succ_pred | [
{
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},
{
"state_after": "no goals",
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1221,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1220,
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Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ContinuousWithinAt.cpow | [] | [
129,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
8
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Mathlib/Logic/Basic.lean | forall₂_swap | [] | [
657,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.measurableSet_sSup | [
{
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501,
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Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_card_le | [] | [
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16
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1614,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_quadratic | [] | [
1201,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
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Mathlib/RingTheory/Localization/Basic.lean | Localization.algEquiv_mk | [
{
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... | [
1079,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Basic.lean | Nat.eq_mul_of_div_eq_left | [
{
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}
] | [
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50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.mem_Lp_of_ae_nnnorm_bound | [] | [
406,
68
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404,
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Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.Chain.map_id | [] | [
140,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
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Mathlib/Algebra/Star/Pointwise.lean | Set.union_star | [] | [
83,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/CategoryTheory/Pi/Basic.lean | CategoryTheory.Pi.isoApp_trans | [] | [
214,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
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Mathlib/Analysis/Calculus/FDeriv/Star.lean | differentiable_star_iff | [] | [
97,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/CategoryTheory/Preadditive/ProjectiveResolution.lean | CategoryTheory.ProjectiveResolution.π_f_succ | [
{
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116,
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.sum_smul_mem | [] | [
252,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
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Mathlib/RingTheory/WittVector/Defs.lean | WittVector.wittNeg_zero | [
{
"state_after": "case a\np : ℕ\nR : Type ?u.70738\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\n⊢ ↑(map (Int.castRingHom ℚ)) (wittNeg p 0) = ↑(map (Int.castRingHom ℚ)) (-X (0, 0))",
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"tact... | [
290,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
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Mathlib/Topology/Separation.lean | disjoint_nested_nhds | [
{
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1684,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1677,
1
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.separating_of_T1 | [
{
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362,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
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Mathlib/LinearAlgebra/Dual.lean | Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff | [
{
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"tactic": "rw [← SetLike.ext_iff.mp dualAnnihilator_dualCoannihilator_eq v... | [
982,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
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Mathlib/Tactic/CategoryTheory/BicategoryCoherence.lean | Mathlib.Tactic.BicategoryCoherence.assoc_liftHom₂ | [] | [
315,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.degree_div_le | [
{
"state_after": "no goals",
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"tactic": "simp [hq]"
},
{
"state_after": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\nin... | [
266,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
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Mathlib/Data/Fin/Basic.lean | Fin.antitone_iff_succ_le | [] | [
1904,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1902,
1
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Mathlib/Analysis/InnerProductSpace/Orientation.lean | OrthonormalBasis.det_to_matrix_orthonormalBasis_of_same_orientation | [
{
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63,
11
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57,
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Mathlib/Topology/PathConnected.lean | Path.trans_cast | [] | [
478,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
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Mathlib/Combinatorics/Colex.lean | Colex.empty_toColex_le | [
{
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"state_before": "α : Type u_1\ninst✝ : LinearOrder α\nA : Finset α\n⊢ toColex ∅ ≤ toColex A",
"tactic... | [
358,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | mem_vectorSpan_pair_rev | [
{
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"tactic": "rw [vectorSpan_pair_rev... | [
1289,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1287,
1
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.exists_fixed_point_of_prime | [
{
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"tactic": "classical\n contrapose! hα\n simp_rw [← mem_support, ← Finset.eq_univ_iff_forall] at hα\n exact Nat.m... | [
342,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
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Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.not_mem_bot | [] | [
187,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_update_ne | [
{
"state_after": "no goals",
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"tactic": "rw [p.coeff_update_apply, if_neg h]"
}
] | [
1102,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_insert_insert_insert_of_mem_affineSpan_pair | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\nι : Type ?u.326734\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np₁ p₂ p₃ p₄ p₅ : P\nh₁ : p₁ ∈ affineSpan k {p₄, p₅}\nh₂ : p₂ ∈ affineSpan k {p₄, p₅}\nh₃ : p₃ ∈ affineSpan k {p₄, p₅}\n⊢ Collinear k {p₄... | [
581,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
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Mathlib/Algebra/Order/Group/Defs.lean | Right.inv_lt_one_iff | [
{
"state_after": "no goals",
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"tactic": "rw [← mul_lt_mul_iff_right a, inv_mul_self, one_mul]"
}
] | [
284,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
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Mathlib/NumberTheory/RamificationInertia.lean | Ideal.inertiaDeg_of_subsingleton | [
{
"state_after": "R : Type u\ninst✝¹ : CommRing R\nS : Type v\ninst✝ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\nhp : IsMaximal p\nhQ : Subsingleton (S ⧸ P)\nthis : P = ⊤\n⊢ inertiaDeg f p P = 0",
"state_before": "R : Type u\ninst✝¹ : CommRing R\nS : Type v\ninst✝ : CommRing S\nf : R →+* S\np : Ide... | [
208,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_multiset_sum | [] | [
2049,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2047,
1
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Std/Data/Int/Lemmas.lean | Int.sub_sub_self | [
{
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"state_before": "a b : Int\n⊢ a - (a - b) = b",
"tactic": "simp [Int.sub_eq_add_neg, ← Int.add_assoc]"
}
] | [
367,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
366,
11
] |
Mathlib/Data/FunLike/Basic.lean | FunLike.coe_eq_coe_fn | [] | [
159,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/QPF/Multivariate/Basic.lean | MvQPF.liftP_iff | [
{
"state_after": "case mp\nn : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\np : ⦃i : Fin2 n⦄ → α i → Prop\nx : F α\n⊢ LiftP p x → ∃ a f, x = abs { fst := a, snd := f } ∧ ∀ (i : Fin2 n) (j : MvPFunctor.B (P F) a i), p (f i j)\n\ncase mpr\nn : ℕ\nF : TypeVec n → Type u_1\ninst✝ : ... | [
141,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Std/Logic.lean | not_and_of_not_right | [] | [
233,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
233,
1
] |
Mathlib/Algebra/Order/Monoid/WithZero/Defs.lean | WithZero.zero_eq_bot | [] | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Tactic/CategoryTheory/Reassoc.lean | CategoryTheory.eq_whisker' | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝ : Category C\nX Y : C\nf g : X ⟶ Y\nw : f = g\nZ : C\nh : Y ⟶ Z\n⊢ f ≫ h = g ≫ h",
"tactic": "rw [w]"
}
] | [
35,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Analysis/Convex/StrictConvexSpace.lean | not_sameRay_iff_norm_add_lt | [] | [
223,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.ι_toSubtype | [
{
"state_after": "case w\nJ : Type w\nC : Type u\ninst✝⁴ : Category C\ninst✝³ : HasZeroMorphisms C\nf : J → C\ninst✝² : HasBiproduct f\np : J → Prop\ninst✝¹ : HasBiproduct (Subtype.restrict p f)\ninst✝ : DecidablePred p\nj : J\n⊢ ∀ (j_1 : Subtype p),\n (ι f j ≫ toSubtype f p) ≫ π (Subtype.restrict p f) j_1 =... | [
626,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieIdeal.comap_bracket_incl | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nf : L →ₗ⁅R⁆ L'\nI : LieIdeal R L\nJ : LieIdeal R L'\nI₁ I₂ : LieIdeal R L\n⊢ ⁅comap (incl I) I₁, comap (incl I) I₂⁆ =\n comap (incl I) ⁅LieHo... | [
341,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter₂_union | [
{
"state_after": "no goals",
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1026,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
1
] |
Mathlib/CategoryTheory/GradedObject.lean | CategoryTheory.GradedObject.comapEq_trans | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nβ γ : Type w\nf g h : β → γ\nk : f = g\nl : g = h\n⊢ comapEq C (_ : f = h) = comapEq C k ≪≫ comapEq C l",
"tactic": "aesop_cat"
}
] | [
112,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Algebra/Tropical/BigOperators.lean | List.untrop_prod | [
{
"state_after": "case nil\nR : Type u_1\nS : Type ?u.9353\ninst✝ : AddMonoid R\n⊢ untrop (prod []) = sum (map untrop [])\n\ncase cons\nR : Type u_1\nS : Type ?u.9353\ninst✝ : AddMonoid R\nhd : Tropical R\ntl : List (Tropical R)\nIH : untrop (prod tl) = sum (map untrop tl)\n⊢ untrop (prod (hd :: tl)) = sum (map... | [
67,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | MonoidHom.apply_mint | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.347165\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : Group M\nf : Multiplicative ℤ →* M\nn : Multiplicative ℤ\n⊢ ↑f n = ↑f (↑Multiplicative.ofAdd 1) ^ ↑Multiplicative.toAdd n",
"tactic"... | [
907,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix₂_symm | [] | [
399,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Order/WithBot.lean | WithBot.toDual_le_iff | [] | [
978,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.ofFractionRing_smul | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝¹ : CommRing K\nR : Type u_1\ninst✝ : SMul R (FractionRing K[X])\nc : R\np : FractionRing K[X]\n⊢ { toFractionRing := c • p } = c • { toFractionRing := p }",
"tactic": "simp only [SMul.smul, HSMul.hSMul, RatFunc.smul]"
}
] | [
449,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.OuterMeasure.pi_pi_le | [
{
"state_after": "case inl\nι : Type u_2\nι' : Type ?u.1844425\nα : ι → Type u_1\ninst✝ : Fintype ι\nm✝ m : (i : ι) → OuterMeasure (α i)\ns : (i : ι) → Set (α i)\nh : Set.pi univ s = ∅\n⊢ ↑(OuterMeasure.pi m) (Set.pi univ s) ≤ ∏ i : ι, ↑(m i) (s i)\n\ncase inr\nι : Type u_2\nι' : Type ?u.1844425\nα : ι → Type u... | [
204,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.iInter_Ioi_coe_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.137733\nβ : Type ?u.137736\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ (⋂ (n : ℕ), Ioi ↑n) = {⊤}",
"tactic": "simp only [← compl_Iic, ← compl_iUnion, iUnion_Iic_coe_nat, compl_compl]"
}
] | [
899,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullbackDiagonalMapIso_hom_snd | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\nX Y Z : C\ninst✝¹ : HasPullbacks C\nU V₁ V₂ : C\nf : X ⟶ Y\ni : U ⟶ Y\ni₁ : V₁ ⟶ pullback f i\ni₂ : V₂ ⟶ pullback f i\ninst✝ : HasPullback i₁ i₂\n⊢ (Iso.mk (lift (snd ≫ fst) (snd ≫ snd) (_ : (snd ≫ fst) ≫ i₁ = (snd ≫ snd) ≫ i₂))\n (lift (fst ≫ i₁ ≫ f... | [
165,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Std/Data/Array/Lemmas.lean | Array.get!_eq_getD | [] | [
65,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
65,
1
] |
Mathlib/Data/Sum/Order.lean | WithTop.orderIsoSumLexPUnit_top | [] | [
784,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Topology/ContinuousOn.lean | eventually_nhdsWithin_nhdsWithin | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3293\nγ : Type ?u.3296\nδ : Type ?u.3299\ninst✝ : TopologicalSpace α\na : α\ns : Set α\np : α → Prop\nh : ∀ᶠ (y : α) in 𝓝[s] a, ∀ᶠ (x : α) in 𝓝[s] y, p x\n⊢ ∀ᶠ (x : α) in 𝓝[s] a, p x",
"state_before": "α : Type u_1\nβ : Type ?u.3293\nγ : Type ?u.3296\nδ : Type ... | [
72,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.terminal.subsingleton_to | [] | [
255,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.indicator | [] | [
813,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
11
] |
Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean | CategoryTheory.MonoidalOfChosenFiniteProducts.leftUnitor_naturality | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX Y : C\n𝒯 : LimitCone (Functor.empty C)\nℬ : (X Y : C) → LimitCone (pair X Y)\nX₁ X₂ : C\nf : X₁ ⟶ X₂\n⊢ IsLimit.lift (ℬ 𝒯.cone.pt X₂).isLimit\n (BinaryFan.mk (BinaryFan.fst (ℬ 𝒯.cone.pt X₁).cone ≫ 𝟙 𝒯.cone.pt) (BinaryFan.snd (ℬ 𝒯.cone.pt X₁).cone ... | [
312,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/LinearAlgebra/AdicCompletion.lean | adicCompletion.eval_of | [] | [
244,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.of_a_eq_zero' | [] | [
145,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Topology/Support.lean | tsupport_smul_subset_left | [] | [
104,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.classes_ker_subset_fiber_set | [
{
"state_after": "case intro\nα : Type u_2\nβ : Type u_1\nf : α → β\nx : α\n⊢ {x_1 | Rel (ker f) x_1 x} ∈ Set.range fun y => {x | f x = y}",
"state_before": "α : Type u_2\nβ : Type u_1\nf : α → β\n⊢ classes (ker f) ⊆ Set.range fun y => {x | f x = y}",
"tactic": "rintro s ⟨x, rfl⟩"
},
{
"state_af... | [
85,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_sq_eq_abs | [
{
"state_after": "no goals",
"state_before": "x✝ y x : ℝ\n⊢ sqrt (x ^ 2) = abs x",
"tactic": "rw [sq, sqrt_mul_self_eq_abs]"
}
] | [
250,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | comm_topologicalGroup_is_uniform | [
{
"state_after": "G : Type u_1\ninst✝² : CommGroup G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nthis :\n Tendsto ((fun p => p.fst / p.snd) ∘ fun p => (p.fst.snd / p.fst.fst, p.snd.snd / p.snd.fst))\n (comap (fun p => (p.fst.snd / p.fst.fst, p.snd.snd / p.snd.fst)) (Filter.prod (𝓝 1) (𝓝 1)))... | [
685,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.ker_rangeRestrict | [] | [
2825,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2824,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.repr_ker | [
{
"state_after": "no goals",
"state_before": "ι : Type u'\nι' : Type ?u.440821\nR : Type u_2\nK : Type ?u.440827\nM : Type u_1\nM' : Type ?u.440833\nM'' : Type ?u.440836\nV : Type u\nV' : Type ?u.440841\nv : ι → M\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M'\ninst✝³ : AddCommGroup M''... | [
791,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.map_continuous | [] | [
315,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reflect_C | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\nr : R\nN : ℕ\n⊢ reflect N (↑C r) = ↑C r * X ^ N",
"tactic": "conv_lhs => rw [← mul_one (C r), ← pow_zero X, reflect_C_mul_X_pow, revAt_zero]"
}
] | [
163,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
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